Optimale Transaktions-, Vorsichts- und Spekulationskasse

Abstract

Optimal Transaction, Precautionary and Speculative Cash. Discussion of Some Solution Approaches

In this article possible solutions for determining optimal transaction cash, optimal precnationary cash and optimal specnlative cash are discussed. Optimal transaction cash is calculated on the basis of the Baumol-Tobin inventory theory approach (premisses: complete information on the inpayment/ out-payment pattern, credit and security interest rates, allowances for cash - securities - cash transaction costs). The models of optimal precuationary cash authored by Patinkin, Whalen and Sprenkle, which are discussed here, have defects. In Patinkin’s model no convincing objective function is discernible, in Whalen’s the cash - securities - cash transaction costs and hypotheses concerning in-payment/out-payment patterns are lacking, and Sprenkle’s precautionary cash is not optimal because information costs are not taken into account. A model is developed which avoids these disadvantages and proceeds from the premisses: complete information on security interest rates, but imperfect information on the in-payment/out-payment pattern, and allowances for transaction, illiquidity and information costs. Optimal speculative cash is determined as part of an optimal portfolio. The analysis proceeds from efficient portfolios; weighting of the efficient port folios by a utility function with the arguments of expected return and risk results in the optimal portfolio and hence in the optimal speculative cash, which is calculated with and without allowances for transaction costs. Attention is drawn to the unsatisfactory situation of a dichotomy of cash holdings and basic possibilities of finding a solution are indicated.